It's a brave politician who tries to sell potential voters "fiscal devolution". But if they try to sell its products – increased prosperity, more jobs and improved housing – they might be on to something.

That's how London and England's eight other largest cities have sought to capture the imagination of policymakers. And if the policymakers buy it, and put it in their election manifestos, the public will be next in their sights.

But let's take a step back. What is the evidence for devolution leading to growth? What would happen to people who didn't live in a core city or in its surrounding areas? And how would local councils collaborate to make the day-to-day administration in a city region work? My colleagues on the Communities and Local Government Committee, representing towns, cities and villages throughout England, intend to find out.

The city deals are a good step forward and cities minister Greg Clark has just announced another round of them, but there is a groundswell for something more radical. Along with London, the cities of Birmingham, Sheffield, Manchester, Leeds, Newcastle, Nottingham, Liverpool and Bristol all want to loosen the reins held by Whitehall and to have the freedom to raise money to keep and spend locally. They already have the people and the ideas that can make cities successful. Now they want more control over the money.

The recent London finance commission report and the core cities' prospectus for growth argued that, if they could borrow more money to spend on infrastructure, set and retain property taxes and hold on to more of their business rates, these cities could create municipal centres of innovation and industry to rival those of the 19th century. Indeed, with their proposals on housebuilding and locally-owned energy companies, the resemblance to the civic politics of the Victorian era is even more marked.

But English cities directly control a lot less money than many of their foreign counterparts. Currently, English cities control around 5% of the money raised in taxes from local people, with 95% going to central government. In many successful countries, such as China, Germany and the US, large cities – and not just the capital city – have led economic growth. In England only London consistently outperforms the national economy, contributing 25% of national GDP while England's core cities contribute 18%.

The argument goes that if our cities are set free to control their own finances they will prosper – and so will our country. But is a country really prosperous if certain areas race ahead while the rest make do with low or no growth? Not everyone lives in a city – and certainly not in London or a core city. What happens to them?

People living in rural areas, in our smaller cities, our market towns and villages, will have to be taken into account or the proceeds of devolution will be confined to cities. England's local government finance structure, with its system of equalisation and redistribution measures, is complex enough already. How would it change to take account of fiscal devolution to cities but ensure fairness?

My colleagues and I also want to know what guarantees there are that greater fiscal freedom for cities would improve the health and wealth of local people and not just lead to higher taxes and poorer services. These powers would bring opportunity – including the opportunity to make mistakes. Who picks up the tab for them?

One further question that will need to be examined is how cities would be held to account for the increased powers. Is the public going to be happy with combined authorities – quasi-regional bodies of indirectly elected politicians – taking on these powers? Where would local enterprise partnerships fit in? My committee recently recommended limited reforms to the London Assembly so that it could hold the mayor of London to account for the substantial powers invested in him. But the government was reluctant to accept any re-balancing, however small. If the same is true of cities with increased powers, we could have more powerful local politicians but no corresponding increase in accountability.

At this stage in our inquiry we have many questions and are looking for answers. We want to hear from those involved and likely to be affected: the business that would have a greater proportion of its business rates spent locally; the council that would have increased powers and greater responsibilities; the residents within cities, on cities borders' and in more rural areas.

If the claims of the core cities are correct, fiscal devolution could help generate £222bn by 2030 – the equivalent of adding the economy of Denmark to the UK, and a lot more prosperity and jobs. But this "if" is what needs to be examined.

Clive Betts is Labour MP for Sheffield South East and chair of the communities and local government select committee.